Iraqi soldiers near Youssifiyah, Iraq, searching for US troops who went missing after they were attacked whilst on patrol on Saturday. Photograph: Haidar Fatehi/AP

Thousands of US troops supported by helicopters and planes were last night searching for three soldiers captured by al-Qaida near Baghdad as violence again hit dozens of ordinary Iraqis across the country.

The Islamic State in Iraq - an al-Qaida affiliate - said on its website that it was holding "crusader" soldiers after four others and an interpreter were confirmed killed in fighting on Saturday in the Mahmudiya area in the Sunni "triangle of death" south of the capital.

Last June al-Qaida captured two American soldiers at a checkpoint in nearby Yusufiya, then killed them before they mutilated and booby-trapped their bodies. Major-General William Caldwell, spokesman for the US military, confirmed that three soldiers were missing.

The announcement came on yet another bloody day, with 50 civilians reported killed and 120 injured in a suicide bombing in Makhmour, a Kurdish area in the north. The attack, which badly damaged the office of the Kurdistan Democratic Party of Massoud Barzani, was the second in Kurdish areas in four days.

Elsewhere, four other people were killed and 40 hurt in a bombing in Baghdad's Sadriya market, the scene of many previous attacks.

On the diplomatic front, Iran formally requested talks about Iraq with the US just a week after its foreign minister failed to meet Condoleezza Rice, the US secretary of state, when they were both attending a summit in Egypt.

Iran's foreign ministry said it had sent a formal request for a meeting via the Swiss embassy - the US and Iran have had no diplomatic relations since the 1979 revolution - "to lessen the suffering of the Iraqi people". But there was only a lukewarm response from Dick Cheney, the US vice-president. He spent the day in Cairo at the end of a week long Middle Eastern tour which saw him issue several warnings to Tehran while seeking to bolster Arab support for the US security "surge" in Iraq.

Iran has been pressing the US for talks that would include its aspirations for developing nuclear power, though it has ignored a demand by the UN that it cease uranium reprocessing and enrichment (which can make weapons-grade material). Washington and Tehran are also at odds over Lebanon and Palestine as well as Iraq, where Iran is backing Shia militias and parties.

"We are willing to have that conversation limited to Iraq issues at the ambassador level," said Mr Cheney's spokeswoman. Any meeting is likely to be in Baghdad, as was a previous one in March.

In a striking piece of political timing, the Iranian president, Mahmoud Ahmadinejad, yesterday followed Mr Cheney in visiting the United Arab Emirates, where the US vice-president had been on Saturday.

"We all wish that foreign troops would leave the region and give a chance to countries in the region to establish security themselves," Mr Ahmadinejad said during a meeting with Sheikh Khalifa bin Zayed, the UAE president. "With each other's help, we can turn the Persian Gulf to the gulf of peace and friendship."

The two-day visit to Abu Dhabi is the first by an Iranian president since 1979.

Iran and the UAE have close economic ties but have been at odds since the Shah's day over Iran's annexation of three small islands - Abu Musa, and the Greater and Lesser Tumbs - when the British withdrew from the region in 1971.

Speaking on the deck of the USS John Stennis, one of two aircraft carriers in the Gulf, Mr Cheney declared: "We'll stand with others to prevent Iran from gaining nuclear weapons and dominating this region."

But Iran's defence minister, Mostafa Mohammad Najjar, said: "I warn Mr Cheney and other American leaders that response by the Iranian nation and its armed forces to any military option will be strong, swift and surprising."